Suppose a nationwide study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76. You believe that the figure is higher in your area. You decide to test this claim by randomly calling gasoline stations in your area. Your random survey of 25 stations produced the following prices as shown in the table below. Assume gasoline prices for a region are normally distributed. Do the data you obtained provide enough evidence to support your belief that the average price for a gallon of self-serve regular unleaded gasoline is higher in your area? Use a 1% level of significance. Interpret your result. $3.87 $3.89 $3.76 $3.80 $3.97 3.80 3.83 3.79 3.80 3.84 3.76 3.67 3.87 3.69 3.95 3.75 3.83 3.74 3.65 3.95 3.81 3.74 3.74 3.67 3.70 The appropriate test should be: a right-hand-side tailed t-test to find out if the mean unleaded gasoline price in your area is higher than the national average of $3.76 per gallon. a right-hand-side tailed Z-test for the proportion of gasoline price in your area that is higher than the national average of $3.76 per gallon. a left-hand-side tailed t-test to find out if the mean unleaded gasoline price in your area is higher than the national average of $3.76 per gallon. a Chi-square test for the mean unleaded gasoline price in your area. The appropriate observed value or test statistic is 2.1391 2.5752 1.9578 2.1782 The appropriate critical value is, under a 10% level of significance? 1.485 1.318 2.492 2.101 Is it true that the true average unleaded gasoline price in your area is higher than the national average of $3.76, based on the results of your test? Yes. No, sample evidence does not support this statement. Can’t decide.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a nationwide study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76. You believe that the figure is higher in your area. You decide to test this claim by randomly calling gasoline stations in your area. Your random survey of 25 stations produced the following prices as shown in the table below. Assume gasoline prices for a region are normally distributed. Do the data you obtained provide enough evidence to support your belief that the average price for a gallon of self-serve regular unleaded gasoline is higher in your area? Use a 1% level of significance. Interpret your result.

$3.87	$3.89	$3.76	$3.80	$3.97
3.80	3.83	3.79	3.80	3.84
3.76	3.67	3.87	3.69	3.95
3.75	3.83	3.74	3.65	3.95
3.81	3.74	3.74	3.67	3.70

The appropriate test should be:
a right-hand-side tailed t-test to find out if the mean unleaded gasoline price in your area is higher than the national average of $3.76 per gallon.
a right-hand-side tailed Z-test for the proportion of gasoline price in your area that is higher than the national average of $3.76 per gallon.
a left-hand-side tailed t-test to find out if the mean unleaded gasoline price in your area is higher than the national average of $3.76 per gallon.
a Chi-square test for the mean unleaded gasoline price in your area.

The appropriate observed value or test statistic is
2.1391
2.5752
1.9578
2.1782

The appropriate critical value is, under a 10% level of significance?
1.485
1.318
2.492
2.101

Is it true that the true average unleaded gasoline price in your area is higher than the

national average of $3.76, based on the results of your test?

Yes.
No, sample evidence does not support this statement.
Can’t decide.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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